A man can do a certain task in 21 hours, another man can do the task in 28 hours and a boy can do the task in 48 hours. Find how long it will take to do the task if all three work.

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  1. Try figuring out how much of the task each man can do in one hour, as a fraction.

    You can use that to find out the work done in an hour if all three work together, and thus the amount of time it will take.

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  2. Man 1/21 other man 1/28 boy 1/48
    Man’s rate other man’s rate boy’s rate
    1/21 1/28 1/48
    Let x be the number of hours it will take all three
    to do the task.
    Combined rate = 1/x
    1/21 + 1/28 + 1/48 =
    LCD = 28, 224
    1344 / 28, 224 + 1008 / 28, 224 + 588 / 28, 224
    = 2 940 / 28, 224 or 735 / 7056
    1/x = 735/7056
    Cross multiply
    735x = 7056
    x = 7056/735
    x = 9.6 or 9 hours and 10 minutes

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